Prince William, the Duke of Cambridge and his wife Catherine, Duchess of Cambridge, receives flowers upon their arrival at Changi International Airport in Singapore (EPA)

The Duchess is known to have bought outfits from the outlet centre in Bicester, which has become a regular stop-off for tourists from Japan and the Far East on the well-worn coach route from London to Oxford, but it the first time she has discussed it.

The Royal couple arrived at Changi Airport at 2.50pm local time (07.50BST) on a scheduled British Airways flight from Heathrow at the beginning of a trip where they will act as representatives of the Queen to celebrate Her Majesty's Diamond Jubilee.

They were greeted at the airport by the British High Commissioner, Antony Phillipson, Singapore’s head of protocol Michael Tan and Dr Maliki Osman, Singapore’s senior parliamentary secretary for defence and national development.

Dr Osman said the couple told him they were "excited" to have arrived.

He said: “It's a great honour to have them here in Singapore, for them to be starting their tour here.

“William said he has friends here and he's been told there are lots of wonderful things to see.

“They said they were excited to be here and looking forward to the visit.”

It was Dr Osman’s wife, Sadiah Bte Shahal, who presented the Duchess with the bouquet of tiger orchids and golden shower orchids.

She said: "They are such a lovely couple, so affable. Kate was asking me about my children, what their ages are.”

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The Royal visit has generated huge excitement in Singapore, where more than 170 local journalists are being joined by 90 foreign journalists from the UK, the US, Australia, New Zealand, Japan, Germany, China, France, Indonesia and the Netherlands.

Mr Phillipson said: “This is a couple who are global superstars and who make Singapore feel good about itself.”

The couple had no time to get over jet lag from their 14-hour journey as they headed off to begin a busy day of engagements.

Their first stop was at the National Botanical Gardens, where they were presented with a species of orchid named after them.

The Duke smiled as he was shown the Vanda William Catherine hybrid and told his wife that the orchid’s white petals with purple spots matched her pale pink kimono-style dress by the British designer Jenny Packham, which featured an orchid print.

The garden’s chief executive, Poon Hong Yuen, who showed the couple around, said: “The Duke was joking that it seemed well coloured to match the Duchess’s dress, which seemed true.”

The Duke and Duchess were also shown a white orchid named after Diana, Princess of Wales, which she had been due to see on a visit to Singapore which would have taken place in mid-September 1997 had she not died the month before.

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The Duke said: “It’s beautiful, it’s beautiful,” as it was pointed out to him, and asked if his mother had ever been to Singapore. Mr Poon told him the orchid Dendrobium Memoria Princess Diana had been named in his mother’s absence at a ceremony on Sep 22, 1997. The Duke said: “That’s very nice.”

Singapore is a member of the Commonwealth but it is not a Commonwealth realm, meaning the Queen is not the head of state. The tour is primarily a celebration of the Queen’s Diamond Jubilee, but the Royal couple will also act as trade ambassadors at certain events, as members of the Royal family share out visits which would have been undertaken by the Duke of York before he stepped down from his role as Special Representative for UK Trade and Investment last year.

Following their visit to the Botanic Gardens, the couple arrived at Raffles Hotel where they will be staying for the duration of their three nights in Singapore. A crowd of around 200 people gathered outside the hotel to cheer their arrival.

They were welcomed by the general manager, Pierre Jochem, and the hotel manager, Laurent Branover. The Duchess was presented with a bunch of yellow, white and pink orchids by Lynn Choy, the daughter of Mrs Annie Choy, the hotel's director of marketing. "They are beautiful, thank you," said the Duchess, laughing along with the female staff in the greeting line-up who commented on the matching orchids on her dress.

The Duke of Cambridge told the welcome line up that it had been "a very long flight, but we're so happy to be here".

Mrs Andrea Greybanks, the hotel's director of sales and marketing, who also welcomed the couple, said: "I told her she looked beautiful and she thanked me. Prince William said that he was also very pleased to be following in his grandmother's footsteps by staying with us." The Queen stayed at Raffles during her visit to Singapore in March 2006.

The hotel does not have a "royal suite" and hotel staff would not comment on the couple's accommodation, though it is believed they will be staying in one of Raffles' palatial suites.

Raffles opened in 1887 and was named after Sir Stamford Raffles, the founder of Singapore. Previous guests include Elizabeth Taylor, Ava Gardner and Rudyard Kipling.

Later today, the couple will visit the Istana, the official residence of the President of Singapore, which also houses the office of the Prime Minister.

After reviewing a guard of honour and spending an hour chatting to the President, Tony Tan Keng Yam, and Prime Minister, Lee Hsien Loong, the couple will attend a state reception and dinner, where the Duke will make his first speech of the tour.

The Duke and Duchess will also visit Kuala Lumpur, the rain forests of Borneo, and the Commonwealth realms of the Solomon Islands and the tiny Pacific island of Tuvalu during the trip, their second foreign tour together.